Solve (a^{2}-2a^{3}+3a^{3}-a+7)+(2a^{4}-3a^{3}+2a^2-a+6)+(a^4-2a^3+2a^2-5)=

$$( a ^ { 2 } - 2 a ^ { 3 } + 3 a ^ { 3 } - a + 7 ) + ( 2 a ^ { 4 } - 3 a ^ { 3 } + 2 a ^ { 2 } - a + 6 ) + ( a ^ { 4 } - 2 a ^ { 3 } + 2 a ^ { 2 } - 5 ) =$$

Evaluate

$$3a^{4}-4a^{3}+5a^{2}-2a+8$$

Solution Steps

Combine -2a^{3} and 3a^{3} to get a^{3}.

$$a^{2}+a^{3}-a+7+2a^{4}-3a^{3}+2a^{2}-a+6+a^{4}-2a^{3}+2a^{2}-5$$

Combine a^{3} and -3a^{3} to get -2a^{3}.

$$a^{2}-2a^{3}-a+7+2a^{4}+2a^{2}-a+6+a^{4}-2a^{3}+2a^{2}-5$$

Combine a^{2} and 2a^{2} to get 3a^{2}.

$$3a^{2}-2a^{3}-a+7+2a^{4}-a+6+a^{4}-2a^{3}+2a^{2}-5$$

Combine -a and -a to get -2a.

$$3a^{2}-2a^{3}-2a+7+2a^{4}+6+a^{4}-2a^{3}+2a^{2}-5$$

Add 7 and 6 to get 13.

$$3a^{2}-2a^{3}-2a+13+2a^{4}+a^{4}-2a^{3}+2a^{2}-5$$

Combine 2a^{4} and a^{4} to get 3a^{4}.

$$3a^{2}-2a^{3}-2a+13+3a^{4}-2a^{3}+2a^{2}-5$$

Combine -2a^{3} and -2a^{3} to get -4a^{3}.

$$3a^{2}-4a^{3}-2a+13+3a^{4}+2a^{2}-5$$

Combine 3a^{2} and 2a^{2} to get 5a^{2}.

$$5a^{2}-4a^{3}-2a+13+3a^{4}-5$$

Subtract 5 from 13 to get 8.

$$5a^{2}-4a^{3}-2a+8+3a^{4}$$

Differentiate w.r.t. a

$$12a^{3}-12a^{2}+10a-2$$